Generator switches are usually cooled via natural convection and radiation. If such switches are of unencapsulated design, then the power loss of the conductor is transmitted in the form of heat to an extinction-chamber insulator which contains the contact arrangement of the switch and has cooling ribs led vertically. The heat absorbed by the extinction-chamber insulator is dissipated to the surroundings by convection and radiation. Such generator switches are marketed by ABB High Voltage Technologies Ltd, Zurich/Switzerland under the type designation HEI 1 . . . HEI 5. Furthermore, the abovementioned company also markets generator switches, with the type designation HEC3/HEC4, in which the conductor and the extinction-chamber insulator are arranged in a housing filled with an insulating gas, in particular with air. The heat formed in the conductor and predominantly led to the extinction-chamber insulator is then given up to the housing via natural convection and radiation. In this case, the heat is given up as a result of the temperature differences which become established between the conductor or extinction-chamber insulator the and housing. The heat absorbed by the housing is led off to the surroundings via natural convection and radiation because of the temperature difference between the housing and the surroundings. The heat flow in such a system is automatically established, depends primarily on geometrical dimensions and the materials and surface configurations used and is limited by the mechanisms of heat dissipation. If the generator switch is of threephase design, the three phases being arranged beside one another, the housing of the phase arranged in the center always has the highest temperatures, since the side walls cannot give up any radiation energy, and then has to be cooled particularly intensively.